P-Values and Critical Values

Question

The test statistic of Z = -1.94 is obtained when testing the claim that P = 3/8.

a) Identify the hypothesis test:

b) Find P-value

c) Using a significant level of a = 0.05, should we reject H₀ or should we fail to reject H₀?

d) Find the critical Value (s); should we reject H₀ or should we fail to reject H₀?

Answer 1

a) The test hypotheses are:

H₀: P = 3/8

H₁: P ≠ 3/8

b) Using my TI-83 calculator, the left-hand tail for a Z-score of -1.94 is 0.0262. Since we have a two-sided test, we double this to get a p-value of 0.0524.

c) Since our p-value is greater than the alpha of 0.05, we fail to reject the null hypothesis that P = 3/8.

d) The critical value for a significance of 0.05 on a two-sided test is

Z = 1.96 (memorize this, or use a table or calculator). Since our measured Z-score is lower in absolute value than the critical value, again we fail to reject the null.